Module 1  Describing Functions  
Introduction  Lesson 1  Lesson 2  Lesson 3  Lesson 4  SelfTest  
Lesson 1.4: Describing Functions Numerically  
In Lesson 1.2 you defined the function f(x) = 2x^{2} – 5x – 3 and found its roots symbolically. In Lesson 1.3 you graphed the function and found its roots graphically. In this lesson you will represent the function numerically with a table and use the table to find the roots. Creating a Table of Function Values To make a table of values for a function, you need to enter the function in the Y= Editor. You should have already done this in Lesson 1.3.
Displaying the Table Setup Dialog Box Before you view the table, you should set its parameters.
Table Setup Parameters The value in tblStart will be the first value of x in the table.
The value in tbl determines how much x increases when moving from one row to the next in the table. This value should be 1. Make sure the other settings match the figure shown below, and then press to save all the table parameter values. This should return you to the Y= Editor.
Finding Roots from a Table The table provides numerical evidence for two roots. One root must exist between x = 1 and x = 0 because the corresponding values in y1 change sign and the function is continuous, i.e., it has no breaks. The other root is x = 3 because the corresponding value of y1 is 0. You can get a better approximation of the root between 1 and 0 by changing tbl to 0.1.
You can move up and down within the dialog box with the cursor movement keys . Change the value of tbl to 0.1
Scroll to see the root at –.5 This method of expanding the table between x = 1 and x = 0 is called table zoom. 1.4.1 What root is shown in the table above? Click here for the answer. 

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